Size-Based Ion Selectivity of Micropore Electric Double Layers in Capacitive Deionization Electrodes

Capacitive deionization (CDI) is a fast-emerging technology most commonly applied to brackish water desalination. In typical CDI cells, dissolved ions are removed from the feedwater and stored in electric double layers (EDLs) within micropores of electrically charged porous carbon electrodes. Recent experiments have demonstrated that porous carbon CDI electrodes exhibit selective ion removal based on ion size, with the smaller ion being preferentially removed in the case of equal-valence ions. However, state-of-the-art CDI theory does not capture this observed selectivity, as it assumes volume-less point ions in the micropore EDLs. We here present a theory which includes multiple counterionic species, and relaxes the point ion assumption by incorporating ion volume exclusion interactions into a description of the micropore EDLs. The developed model is a coupled set of nonlinear algebraic equations which can be solved for micropore ion concentrations and electrode Donnan potential at cell equilibrium. We show that our model predicts the non-unity separation factor observed experimentally in CDI systems with two equal-valence counterions, which could not be explained by previous CDI theory. Further, our theory captures the measured values of the separation factor when using the hard-sphere diameter as an adjustable parameter.